The present invention relates to image reconstruction, and more particularly to tomographic image reconstruction in medical imaging.
Tomographic image reconstruction refers to reconstructing an image from a set of projection measurements that are described by a Radon transform. The Radon transform provides a mathematical basis for reconstructing tomographic images from measured projection data. The Radon transform of an image is commonly referred to as a sinogram. Tomographic image reconstruction reconstructs an image by determining pixel values based on the sinogram of the projection data. This is described in greater detail in A. Kak and M. Slaney, Principles of Computerized Tomographic Images, IEEE Press, 1988.
In practice, the number and the quality of the projection measurements is often limited, which effects the quality of the images reconstructed from the projection measurements. For example, in medical imaging, low-dose diagnostic tomographic imaging is commonly used to reduce the risks of excessive radiation to a patient, and can greatly restrict the number and quality of projection measurements. Non-iterative reconstruction algorithms do not typically handle the limited projection measurements well, and often produce significant streaking artifacts. One such non-iterative algorithm is the well known Filtered Back Projection (FBP) algorithm, which is described in A. Kak and M. Slaney, Principles of Computerized Tomographic Images, IEEE Press, 1988. Interpolation in Radon space has been proposed to reduce the artifacts in the non-iterative algorithms. However, applying prior knowledge of image shapes and borders in the null space of the projections is typically very difficult.
Iterative methods have achieved better results than the non-iterative methods by incorporating prior knowledge in the image space to regularize the reconstruction in an iterative operation scheme. In such iterative methods, an objective function typically consists of a data fidelity term, which enforces the similarity between the measured sinogram and a forward projection of the reconstructed image, and a regularization term, which enforces the prior knowledge about the signal (e.g. smooth surface with sharp edges). However, the optimization of the objective function is typically based on a gradient descent method. The derivative on the data fidelity term results is a back projection in each iteration, which typically provides blurry results and converges slowly. Furthermore, the step size to update in the gradient-descent direction is usually set small due to convergence issues, which further increases the number of iterations necessary for convergence significantly.